Wanmo Kang

We show the existence of Nash equilibria in a Bertrand oligopoly price competition game using a possibly asymmetric attraction demand model with convex costs under mild assumptions. We show that the equilibrium is unique and globally stable. To our knowledge, this is the first paper to show the existence of a unique equilibrium with both nonlinear demand and nonlinear costs. In addition, we guarantee the linear convergence rate of tatônnement. We illustrate the applicability of this approach wit

In natural language processing, it has been observed recently that generalization could be greatly improved by finetuning a large-scale language model pretrained on a large unlabeled corpus. Despite its recent success and wide adoption, finetuning a large pretrained language model on a downstream task is prone to degenerate performance when there are only a small number of training instances available. In this paper, we introduce a new regularization technique, to which we refer as "mixout", mot

This paper develops rare-event simulation methods for the estimation of portfolio credit risk—the risk of losses to a portfolio resulting from defaults of assets in the portfolio. Portfolio credit risk is measured through probabilities of large losses, which are typically due to defaults of many obligors (sources of credit risk) to which a portfolio is exposed. An essential element of a portfolio view of credit risk is a model of dependence between these sources of credit risk: large losses occu

The measurement of portfolio credit risk focuses on rare but significant large‐loss events. This paper investigates rare event asymptotics for the loss distribution in the widely used Gaussian copula model of portfolio credit risk. We establish logarithmic limits for the tail of the loss distribution in two limiting regimes. The first limit examines the tail of the loss distribution at increasingly high loss thresholds; the second limiting regime is based on letting the individual loss probabili

This paper develops a method for selecting and analysing stress scenarios for financial risk assessment, with particular emphasis on identifying sensible combinations of stresses to multiple factors. We focus primarily on reverse stress testing – finding the most likely scenarios leading to losses exceeding a given threshold. We approach this problem using a nonparametric empirical likelihood estimator of the conditional mean of the underlying market factors given large losses. We then scale con

We study an inventory system under periodic review when excess demand is lost. It is known (Huh et al. 2009) that the best base-stock policy is asymptotically optimal as the lost-sales penalty cost parameter grows. We now show that this result is robust in the following sense: Consider the base-stock level which is optimal in a backordering system (with a per-unit-per-period backordering cost) in which the backorder cost parameter is a function of the lost-sales parameter in the original system.

The problem of fair classification can be mollified if we develop a method to remove the embedded sensitive information from the classification features. This line of separating the sensitive information is developed through the causal inference, and the causal inference enables the counterfactual generations to contrast the what-if case of the opposite sensitive attribute. Along with this separation with the causality, a frequent assumption in the deep latent causal model defines a single laten

In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model—a single asset model with a multidimensional Wishart variance process. Our method is based on analysis of the conditional characteristic function of the log-price given a terminal volatility level. In particular, we found an explicit expression for the conditional characteristic function for the Heston model. Numerical experiments demonstrate that our new method is much faste

Rotating savings and credit association (ROSCA) is a well-known microfinance association widely used in many countries around the world with long histories. By considering extra profits that such a system can provide when compared to banking transactions, we develop optimization problems to achieve an optimal design of a ROSCA. We find that ROSCAs might attract investors when deposit and loan rates from formal banking systems are not favorable. Furthermore, optimal rates and optimal orders to ma

We present an importance sampling procedure for the estimation of multifactor portfolio credit risk for the t -copula model, i.e, the case where the risk factors have the multivariate t distribution. We use a version of the multivariate t that can be expressed as a ratio of a multivariate normal and a scaled chi-square random variable. The procedure consists of two steps. First, using the large deviations result for the Gaussian model in Glasserman, Kang, and Shahabuddin (2005a), we devise and a

We study a hedging problem in a market where traders have various levels of information. The exclusive information available only to informed traders is modelled by a diffusion process rather than discrete arrivals of new information. The asset price follows a jump–diffusion process and an information process affects jump sizes of the asset price. We find the local risk minimization hedging strategy of informed traders. Numerical examples as well as their comparison with the Black–Scholes strate